Feature Learning for High-dimensional Functional Time Series. This project aims to develop new methods and theories for common features on high-dimensional functional time series observed in empirical applications. The significance includes addressing a key gap in adaptive and efficient feature learning, improving forecasting accuracy and understanding forecasting-driven factors comprehensively for empirical data. Expected outcomes involve advances in big data theory and easy-to-implement algori ....Feature Learning for High-dimensional Functional Time Series. This project aims to develop new methods and theories for common features on high-dimensional functional time series observed in empirical applications. The significance includes addressing a key gap in adaptive and efficient feature learning, improving forecasting accuracy and understanding forecasting-driven factors comprehensively for empirical data. Expected outcomes involve advances in big data theory and easy-to-implement algorithms for applied researchers. This project benefits not only advanced manufacturing by finding optimal stopping time for wood panel compression, but also superior forecasting for mortality in demography, climate data in environmental science, asset returns in finance, and electricity consumption in economics. Read moreRead less
Macroeconomic and Financial Modelling in an Era of Extremes. This project aims to develop methods to allow workhorse models in economics and finance to better reflect tail events--low probability extreme events, such as the Global Financial Crisis and the COVID-19 pandemic. It intends to address fundamental technical challenges in the estimation of such models, develop a coherent framework for counterfactual analysis of these models and propose methods to apply these models in a big-data environ ....Macroeconomic and Financial Modelling in an Era of Extremes. This project aims to develop methods to allow workhorse models in economics and finance to better reflect tail events--low probability extreme events, such as the Global Financial Crisis and the COVID-19 pandemic. It intends to address fundamental technical challenges in the estimation of such models, develop a coherent framework for counterfactual analysis of these models and propose methods to apply these models in a big-data environment. Expected outcomes include new insights into the transmission of tail risks in the global economic and financial system. This should provide significant benefits, including guidance to Australian and international policymakers charged with maintaining stability in the face of extreme events.Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100056
Funder
Australian Research Council
Funding Amount
$403,019.00
Summary
Statistical shape analysis using persistent homology. Statistical shape analysis is the quantitative study of variation in geometric shape. An innovative approach applies concepts from algebraic topology in the form of the persistent homology transform. This project aims to prove mathematical theory relating to the persistent homology transform, to develop new statistical theory and methodology, and to apply this theory to a range of applications including the analysis of bird beaks, human skull ....Statistical shape analysis using persistent homology. Statistical shape analysis is the quantitative study of variation in geometric shape. An innovative approach applies concepts from algebraic topology in the form of the persistent homology transform. This project aims to prove mathematical theory relating to the persistent homology transform, to develop new statistical theory and methodology, and to apply this theory to a range of applications including the analysis of bird beaks, human skulls and boundary contours of stem cells. An anticipated goal is the generation of new and significant theoretical results in topological data analysis. Expected outcomes include a topologically motivated platform for shape analysis that is statistically rigorous and has firm mathematical foundations.
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Uncertainty, Risk and Related Concepts in Machine Learning. Machine learning is the science of making sense of data. It does not and cannot remove all risk and uncertainty. This project proposes to study the foundations of how machine learning uses, represents and communicates risk and uncertainty. It aims to do so by finding new theoretical connections between diverse notions that have arisen in allied disciplines. These include risk, uncertainty, scoring rules and loss functions, divergences, ....Uncertainty, Risk and Related Concepts in Machine Learning. Machine learning is the science of making sense of data. It does not and cannot remove all risk and uncertainty. This project proposes to study the foundations of how machine learning uses, represents and communicates risk and uncertainty. It aims to do so by finding new theoretical connections between diverse notions that have arisen in allied disciplines. These include risk, uncertainty, scoring rules and loss functions, divergences, statistics and different ways of aggregating information. By building a more complete theoretical map it is expected that new machine learning methods will be developed, but more importantly that machine learning will be able to be better integrated into larger socio-technical systems.Read moreRead less
Reliable and accurate statistical solutions for modern complex data. This project aims to develop novel methods for reliable and accurate statistical modelling with modern, complex correlated and error-prone data. The project expects to make significant strides towards future-proofing statistical data analysis, equipping practitioners with a suite of robust and computationally efficient methods which provide confidence in the stability and reproducibility of results obtained, while offering guar ....Reliable and accurate statistical solutions for modern complex data. This project aims to develop novel methods for reliable and accurate statistical modelling with modern, complex correlated and error-prone data. The project expects to make significant strides towards future-proofing statistical data analysis, equipping practitioners with a suite of robust and computationally efficient methods which provide confidence in the stability and reproducibility of results obtained, while offering guarantees on their transferability over a range of populations. This will provide important benefits as they are applied in predicting endangered marine species for fisheries conservation, and in enhancing our national understanding of the relationship between education achievement and financial success. Read moreRead less
Novel statistical methods for data with non-Euclidean geometric structure. This project aims to develop new flexible regression models and classification algorithms, along with robust and efficient inference methods, applicable to a wide range of non-Euclidean data types which arise in many fields of science, business and technology. There are serious flaws with currently available methods of analysis for non-Euclidean data. This project expects to transform such analyses by providing new quanti ....Novel statistical methods for data with non-Euclidean geometric structure. This project aims to develop new flexible regression models and classification algorithms, along with robust and efficient inference methods, applicable to a wide range of non-Euclidean data types which arise in many fields of science, business and technology. There are serious flaws with currently available methods of analysis for non-Euclidean data. This project expects to transform such analyses by providing new quantitative tools within a unifying framework. The anticipated project outcomes will be of mathematical interest and valuable in applications such as finance (predicting Australian stock returns); modelling electroencephalography data; Australian geochemical data, relating to sediments; and Australian X-ray tumour image data. Read moreRead less
Discovery Early Career Researcher Award - Grant ID: DE200100435
Funder
Australian Research Council
Funding Amount
$365,039.00
Summary
Modern statistical methods for complex multivariate longitudinal data. The project aims to develop novel approaches for the statistical analysis of large, complex multivariate longitudinal data, and apply them to two datasets to address scientific questions related to the drivers and consequences of poor physical and mental health in Australia, and the spatio-temporal evolution of species assemblages in the Southern Ocean. The project expects to develop new knowledge in the areas of statistical ....Modern statistical methods for complex multivariate longitudinal data. The project aims to develop novel approaches for the statistical analysis of large, complex multivariate longitudinal data, and apply them to two datasets to address scientific questions related to the drivers and consequences of poor physical and mental health in Australia, and the spatio-temporal evolution of species assemblages in the Southern Ocean. The project expects to develop new knowledge in the areas of statistical model building, model selection, and inference for multivariate longitudinal data. This will lead to a suite of modern methods and insights for computationally efficient, mathematically rigorous statistical data analysis that, when applied, should provide significant benefits to public health and ecology.Read moreRead less
Topics in triangulated categories. This project in pure mathematics, more specifically in modern homological algebra, builds on work started by the chief investigator in the last five years. What has already been done has achieved striking results, solving very different problems that have been open for two decades. And there seem to be many directions in which it could be pursued further.
The international mathematical community seems intrigued by what the chief investigator has achieved recen ....Topics in triangulated categories. This project in pure mathematics, more specifically in modern homological algebra, builds on work started by the chief investigator in the last five years. What has already been done has achieved striking results, solving very different problems that have been open for two decades. And there seem to be many directions in which it could be pursued further.
The international mathematical community seems intrigued by what the chief investigator has achieved recently - judging by invitations to give prestigious talks and the feedback at these events. The expected outcome is major progress in our understanding of derived categories, as well as diverse applications. The benefit will be to enhance the international stature of Australian science.Read moreRead less
Groups, piecewise linear representations, and linear 2-representations. This project aims to address fundamental questions at the interface of two central areas of modern mathematics, geometric group theory and higher representation theory. Higher representation theory is a relatively new field, but its tools have already had a tremendous impact on mathematics. The project is expected to use these tools to address outstanding questions in geometric group theory. The expected outcomes of this pr ....Groups, piecewise linear representations, and linear 2-representations. This project aims to address fundamental questions at the interface of two central areas of modern mathematics, geometric group theory and higher representation theory. Higher representation theory is a relatively new field, but its tools have already had a tremendous impact on mathematics. The project is expected to use these tools to address outstanding questions in geometric group theory. The expected outcomes of this project include resolutions of open problems in the theory of Artin groups and the creation of a new subject, the dynamical theory of two-linear groups.Read moreRead less
Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relat ....Moduli, invariants, and algebraisation. This project is in pure mathematics. It aims to address gaps in our
knowledge in the modern geometries and their associated algebraic structures that arise in classification problems that pervade mathematics and its applications.
This project expects to generate new knowledge in modern algebra and geometry.
Expected outcomes of this project include major progress in our
understanding of invariants of derived categories of algebraic stacks and the
relationship between algebraic and other geometries.
The benefit will be to enhance the international stature of Australian science.Read moreRead less